Circle Geometry with tangent

1. The problem statement, all variables and given/known data
I have the circle of equation (x-3)² + (y-4)² = 5²
Find the exact length of the tangents from the point (10,0) to the circle

2. Relevant equations

3. The attempt at a solution

Honestly I cant acutally visualise on a co-oridinate graph what it's asking. A tangent touches the circle at the edge, meeting the radius at a right angle. But what does it mean find the exact lenght of the tangets??

Honestly I cant acutally visualise on a co-oridinate graph what it's asking. A tangent touches the circle at the edge, meeting the radius at a right angle. But what does it mean find the exact lenght of the tangets??

Hi thomas49th!

m_s_a has given a very nice picture of the co-ordinate graph.

But I would find the distance from (10,0) to the centre of the circle, and then use Pythaogras' theorem (twice).

err image had loads of all kinds of stuff i didn't need right? I'm still not sure what im actually finding out. I can see why you use pythagerous make a right angle triangle out of x and y and find the line using a² + b² = c². That's easy... i just dont know what the question is asking

There's nothing wrong with the question. It's just asking for the length of the segment of a tangent that starts at (10,0) and ends at the point tangency. From basic geometry, there are two different tangent lines so you have to find the length of the two different segments.

Remember that the tangent is perpendicular to the radius. Draw a line from (4, 5) to the point of tangency and the line from (4,5) to (10,0) in your picture and you have a right triangle with the line from (4,5) to (10,0) as hypotenuse. You know the length of the radius from (4,5) to the point of tangency and you can calculate the length of the hypotenuse from (4,5) to (10,0). As tiny tim said, use the Pythagorean theorem to find the length of the tangent segment.